A medical team wanted to learn if children between 5 and 17 years old in an area known for high lead contamination have higher lead concentrations in their blood than children between 5 and 17 years old in an area 20 miles away from the first area. (Note: Sampling revealed that lead is only present in the environment at extremely low levels in the second area.) After analyzing blood samples that were collected from children in both regions (under a protocol approved for high ethical standards), an (unpaired/randomized) t-test (data met the assumptions) resulted in a p-value of 0.423. Subsequently, one of the researchers noticed that by chance the ages of the children in the study happened to mean that there was exactly one child of each of the following ages at both of the locations: 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 years old. Therefore, they were able to run a paired analysis, with blocking by age. The data met the assumption of the paired t-test, which yielded a p-value of 0.031. Answer the following questions: a) According to the (unpaired) t-test, what conclusion would the medical team draw? Include the variable names in your answer. b) According to the paired t-test, what conclusion would the medical team draw? Include the variable names in your answer. c) Consider the specific p-values of the two analyses carefully in order to answer the following. Very briefly explain a simple, logical, biological reason why the two tests (unpaired t-test versus paired t-test) yielded very different conclusions. Your explanation should be based in part on the info provided at the beginning of this section (“A medical team…”), and in part on the difference between the two designs on which the two analyses are based.
A medical team wanted to learn if children between 5 and 17 years old in an area known for high lead contamination have higher lead concentrations in their blood than children between 5 and 17 years old in an area 20 miles away from the first area. (Note: Sampling revealed that lead is only present in the environment at extremely low levels in the second area.) After analyzing blood samples that were collected from children in both regions (under a protocol approved for high ethical standards), an (unpaired/randomized) t-test (data met the assumptions) resulted in a p-value of 0.423.
Subsequently, one of the researchers noticed that by chance the ages of the children in the study happened to mean that there was exactly one child of each of the following ages at both of the locations: 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 years old. Therefore, they were able to run a paired analysis, with blocking by age. The data met the assumption of the paired t-test, which yielded a p-value of 0.031.
Answer the following questions:
a) According to the (unpaired) t-test, what conclusion would the medical team draw? Include the variable names in your answer.
b) According to the paired t-test, what conclusion would the medical team draw? Include the variable names in your answer.
c) Consider the specific p-values of the two analyses carefully in order to answer the following. Very briefly explain a simple, logical, biological reason why the two tests (unpaired t-test versus paired t-test) yielded very different conclusions. Your explanation should be based in part on the info provided at the beginning of this section (“A medical team…”), and in part on the difference between the two designs on which the two analyses are based.
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